Communication: The reason why +c ZnO surface is less stable than −c ZnO surface: First-principles calculation

ZnO films are one of the most important oxide materials and have been used to fabricate light emitting devices¹ and quantum Hall effect devices² that are competitive with those made from conventional semiconductors, such as GaN and GaAs. The crystalline structure of ZnO is wurtzite, showing polarity along the c axis. As reported in detail for GaN, polarity is one of the most important factors in film growth, impurity incorporation, and device performance.³ 

We have successfully grown a ZnO film with a smooth surface on an a-plane (⁠|$11\bar 20$|$112¯0$⁠) sapphire substrate by metalorganic chemical vapor deposition in H₂ ambient.⁴ The polarity was determined to be the O(−c) surface, like that of ZnO films grown on sapphire substrates by MBE,⁵ sputtering,⁶ and pulsed laser deposition (PLD).¹ The film growth along the −c polar direction has been explained by a first-principles calculation about the interface structure between ZnO and c-plane (0001) sapphire substrate.⁷ Growth of a ZnO film along the Zn(+c) polar direction allows incorporation of enough nitrogen to achieve p-type conduction.^8,9 Although we attempt to grow a ZnO film homoepitaxially on the +c surface of a bulk ZnO substrate, the surface of the substrate was damaged at around 400 °C during ramping of the substrate temperature in H₂ ambient before starting deposition.

Although it is important to understand the reasons and mechanisms of the polar surface stability to gain insights into films growth, the reason for the dependence of the stability on the polarity of ZnO in H₂ ambient has remained unclear. In this study, we performed a comprehensive study of the optimized structure of a polar surface terminated with various H atom coverages in order to consider a favorable polar direction for ZnO film growth.

The density functional theory calculations were executed with the DMol3 program package.¹⁰ The PW91 functional¹¹ with a double-numeric polarized basis set and effective core potential¹² was employed with a smearing factor of 0.01 a.u., octupole multipolar expansion with a global-space cutoff of 4.4 Å, and a Monkhorst-pack grid of 4 × 2 × 1 for the k-space representation. The structure of the ZnO polar surface region consisted of 32 zinc and 32 oxygen atoms (corresponding to two unit cell layers) with ZnO(0001) and ZnO(⁠|$000\bar 1$|$0001¯$⁠) surfaces. The c and a lattice constants of ZnO in the model were 5.207 and 3.250 Å, respectively,¹³ which are comparable with experimental values. Up to now, theoretical calculations have been focused on both the Zn-terminated +c surface and the O-terminated −c surface.^14–17 The influence of H and O (Ref. 16) and H₂O (Ref. 17) on the polar surface has mainly been calculated for the O-terminated −c surface, whereas there have been few reports of H atom termination on the +c surface. Zn is easily oxidized, and the growth rate of high-quality ZnO film is limited by controlling the supply amount of Zn, so that the growth surface must be terminated with oxygen.⁴ Since the same termination atom should be used for direct comparison of polarity dependence, we prepared O-terminated +c and −c surfaces with various H atom coverages (see the inset of Fig. 1). The structure in the top unit cell was optimized to obtain the minimized total energy while keeping the unit cell at the bottom fixed, according to the method in a previous report.¹⁸ Geometry optimization was performed while varying the H atom coverage from 0% to 100% on both polar surfaces. Here, in order to investigate the surface structure of the −c ZnO polar surface under H₂ atmosphere, we performed the first-principles calculations to clarify what would happen to H₂ molecule approaching to O atom terminated −c ZnO polar surface. The calculation results show that H₂ molecule was dissociatively adsorbed on the O atoms of the O atom terminated −c ZnO polar surface without activation barrier and then two OH termination structure were generated. In this communication, we neglect the effect of the inner hydrogen atoms in the bulk ZnO on the stability of the ZnO polar surfaces, because only small amount of H atoms can be intruded into the bulk ZnO and then does not significantly affect the stability of the ZnO polar surfaces.

Figure 1 shows the energy difference (E_ab) of +c and −c ZnO models terminated with H atom with respect to that of a +c ZnO model with no H atom coverage. The value of E_ab was normalized by one hydrogen atom adsorption site in order to avoid size dependency. The structure of the −c surface with 50% H atom coverage was the most stable among all coverage structures, which is consistent with a previous calculation by Meyer.¹⁶ After optimizing the structures of −c surfaces terminated with various H atom coverages, the −c surfaces maintained a wurtzite structure as illustrated in Fig. 2. The distance between the H atom and oxygen atoms (O_i–H_i) was 0.985 Å in the model with 100% H atom coverage (Table I). As the H atom coverage was decreased, the bond distance decreased to 0.973 Å in the case of 50% and 25% coverages, and the bond population increased from 0.61 at 100% coverage to 0.66 at 50% coverage. Also, as the H atom coverage was decreased, the H atom charge increased from +0.15 at 100% coverage to +0.30 for most stable 50% coverage surface, indicating that the atomic-radius of H atoms becomes smaller with decreasing H atom coverage. The positions of H atoms were optimized to minimize repulsion forces between them with lower H atom coverage. For the most stable structure, the influence of the repulsion force and the instability of dangling bonds on oxygen were minimized.

On the other hand, for the +c ZnO model, 75% H atom coverage was the most stable (Fig. 1). However, drastic displacement of surface atoms on the +c surface occurred after the geometry optimization as shown in Fig. 3. As the H atom coverage was decreased, the bond distance (3.250 Å) between two oxygen atoms (O_a–O_b) at 100% coverage decreased to 1.349 Å (Table II), which is nearly equal to the bond distance of 1.22 Å of the O₂ molecule. Although the bond population between two oxygen atoms was 0.00 at 100% coverage, it increased to 0.37 at 75% coverage. These results suggest the formation of O₂ molecules on a +c surface covered partially with H atom. Experimentally, bulk ZnO substrates with +c and −c polarity were annealed in H₂ flow under 200 Torr at various temperatures. Figure 4 shows the AFM images for +c and −c ZnO surfaces after the annealing. Step and terrace structure on +c ZnO surface disappeared after 500 °C annealing, while that on −c surface was maintained even after 500 °C annealing. The difference of damaged temperature among polar surface is consistent with the calculation prediction.

We now discuss the reasons for O₂ molecule formation on the +c surface, which would be one of the reasons of instability. The bonding angles of O–Zn–O for the +c surface at 100% coverage ranged from 106.23° to 116.29°, which can barely maintain a wurtzite structure. However, the angles for the +c surface at 75% coverage were reduced to 87.05° for O_b–Zn_b–O_d and 99.95° for O_c–Zn_c–O_d as listed in Table II. Bond angles of around 110° and 90° correspond to Zn coordination numbers of four and six, respectively. Since it has been reported that a Zn complex has coordination numbers of not only four but also six,¹⁹ we assumed that the change of Zn coordination number must be one of the main reasons for the generation of O₂ molecules. In order to confirm this assumption, we calculated another model with one oxygen atom placed on a Zn-terminated +c surface of wurtzite ZnO.²⁰ After structural optimization, the angle of O–Zn–O was ∼90° (data not shown), corresponding to the coordination number of six of a rock salt structure. If the Zn atoms on the +c surface are partially terminated with oxygen, the bonding configuration should form a rock salt rather than a wurtzite structure. The coordination number of Zn changed from four to six on the +c surface terminated partially with oxygen atoms. Consequently, O₂ molecules were formed, and the +c surface became unstable. These results suggest the possibility that a ZnO film could be epitaxially grown along the +c polar direction just by maintaining 100% H atom coverage to avoid a change in coordination number from four to six. In this case, H atoms are expected to play the role of a surfactant for ZnO growth along the +c polar direction, such as the growth of hydrogenated amorphous silicon films.

In summary, the minimum geometrical energy was calculated for both polar surfaces of ZnO terminated with oxygen for various H atom coverages. The −c surface was more stable than the +c surface, maintaining a wurtzite structure regardless of H atom coverage. On the other hand, Zn atoms on the +c surface exhibited a change in coordination number from four (wurtzite) to six (rock salt). During the change in structure, the oxygen atom on the surface moved to the neighboring oxygen atoms, forming O₂ molecules. This was the reason why the +c surface was less stable than the −c surface. These calculations support the experimental results of favorable −c ZnO film growth and unstable +c ZnO in H₂ ambient.